I just had the same thing happen. I edited some grammar in this SO question, which was re-tagged by the edit previous to mine (which occurred some 14 months earlier). I did not change any tags, but was awarded the "Organizer" badge. I also had over 2k rep at the time.

It seems like it only checked that I edited the question and that the question was re-tagged. I wonder if someone can test to see if you can earn other, potentially similar badges like "Cleanup" in this manner.